Hertzian Contact Simulation Based on PFEM
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Accurate contact prediction of tool and workpiece is a fundamental requirement for physics-based milling simulations, since contact conditions govern local pressure distribution, stiffness at the interface, ultimately cutting forces, and surface integrity. Machining models based on the Finite Element Method (FEM) are widely used [1], however, if material removal and mesh separation are involved, the FEM faces some difficulties. Hence, in this work we present an adapted approach using Particle Finite Element Method (PFEM) [2]. This work presents a contact module as a first building block towards a full milling-process simulation. The simulation framework is implemented in the performance-optimized programming language julia using an updated Lagrangian formulation, combining standard FE formulations with frequent remeshing and geometry detection to track evolving boundaries and contact interfaces [3]. Contact detection is performed through PFEM surface identification, designed to reliably locate the active contact patch as the deformation progresses [4]. This module is validated on the classical Hertzian normal-contact, enabling systematic error assessment [5]. REFERENCES [1] J. Mackerle, Finite-element analysis and simulation of machining: a bibliography (1976–1996), Journal of Materials Processing Technology, Vol.86, pp.17-44, 1999. [2] T. Pore, S. G. Thorat, A. A. Nema, Review of contact modelling in nonlinear finite element analysis,Materials Today: Proceedings, Vol.47, pp.2436–2440, 2021. [3] E. Oñate, S.R. Idelsohn, F. D. Pin and R. Aubry, The Particle Finite Element Method — An Overview, International Journal of Computational Methods, Vol.1, pp.267-307, 2004. [4] M. Schewe, A. Menzel, Aspects of the Particle Finite Element Method applied to contact problems, PAMM, Vol.19, 2019. [5] N. Chandrasekaran, W.E. Haisler and R.E. Goforth, Finite element analysis of Hertz contact problem with friction, Finite Elements in Analysis and Design, Vol.3, pp.39-56, 1987.
